ABSTRACT
Multiple regression analysis is the statistical technique used most widely in data analysis and the development of empirical models. A major contributing factor has been the growth in speed and accessibility of computers. Multiple regression analysis is employed, for example, by the National Weather Service (NWS) in converting the output of numerical models into operational weather forecasts (see Chapter 8). During the past twenty years, there have been a variety of regression techniques proposed in the literature. These techniques will be reviewed briefly and then a detailed discussion of ridge regression and generalized inverse regression will be presented. We focus on these biased estimation procedures because these techniques are most effective in dealing with a serious deficiency of least squares estimation, the inability to produce useful regression models when the predictor variables are highly correlated. It is important to note that many meteorological predictor variables, including some of those used by the NWS in developing weather fore-casting equations based on multiple regression analysis, are necessarily highly correlated because of inherent physical relationships.
